Conflicting faces rendering as black
It's really easy to solve. There are just not enough transparency bounces in your settings.

Just crank up the max. number of Transparency Bounces to say 18 and the problem is gone. EDIT: 18 works for this view. From an other viewing angle you probably need a lot more. This might result in bad render times...

The problem occurs at places, where the ray has to bounce more. Because the max. number of bounces is to low, it draws an black pixel. 



Transparency set to 18 or higher solves the issue